is considered, where \(\hat{n}\)  is a unit vector whose orientation may, in the most general case, be site dependent. We call Eq. REF  the generator of the QFI. In choosing these generators, the key point is that not all generators relative orientation are equivalent. If the generator commutes with the Hamiltonian, then the ground state will be an eigenstate of the generator, and the covariance, and hence the QFI, will be zero. We discuss the implications of this fact for the spin-1 Heisenberg chain more in Sec. . The generator that will detect the greatest QFI is the one for which \([H,\Lambda ]\)  is maximal. Often at the critical point this will be the most relevant operator[1]}.
